Handbook of the History of Logic: - Fordham University Faculty

426 Gyula Klima
a given situation independently from its truth, indeed, independently from its
existence in that situation. This is most obvious in Buridan’s discussion leading
to his final definition of logical validity, where, using the example ‘No proposition
is negative; therefore, some proposition is negative’, he first argues against his
improved definition as follows:
Again, it is not possible for things to be as the first [proposition, i.e.,
the antecedent] signifies without their being as the second [the consequent]
signifies; therefore, the consequence is valid. The consequence
seems to be manifest from what we said a valid consequence was in the
previous sophism, and you cannot otherwise express the reason why
a consequence is said to be valid. But I prove the antecedent: for it
follows that if things are as it signifies, then it signifies; and it follows
that if it signifies, then it is; and, if it is, then things are as signified
by the second. 64
In his reply to this objection, Buridan draws a very important distinction between
two possible ways of understanding his improved definition of validity:
To the second, which seems to be troublesome, I reply that a consequence
is never true or false unless it is; and thus the validity or truth of
a consequence requires that its antecedent and consequent exist. And
then, with this assumption, we give the rule that a consequence is valid
if it is impossible for things to be as the antecedent signifies without
their being as the consequent signifies. And this rule can be understood
in two ways: first, that it is one proposition about impossibility
in the composite sense, in the way that this is commonly used, and its
sense then is that this is impossible: ‘When it is formed, things are as
the antecedent signifies and not as the consequent signifies’. And taken
in this way the rule is not valid, for according to this rule it follows
that the sophism is true. And it is according to this false rule that the
argument proceeded. Taken in the other way, the rule is understood as
a proposition about impossibility in the divided sense, so that its sense
is: a consequence is valid if in whatever way the antecedent signifies
[things to be], it is impossible for things to be in that way without
their being in the way the consequent signifies [them to be]. And it is
clear that this rule would not prove the sophism true, for in whatever
way the proposition ‘No proposition is negative’ signifies, it is possible
for things to be in that way, and yet for them not to be in the way in
which the other signifies; for this would be that case if, while the affirmatives
stayed in existence, all negatives were annihilated, and this is
possible. 65
64 SD, pp. 956-957.
65 SD, pp. 957-958.